TY - JOUR

T1 - On matrix characterizations for P-property of the linear transformation in second-order cone linear complementarity problems

AU - Miao, Xin He

AU - Chen, Jein Shan

N1 - Funding Information:
The author's work is supported by National Natural Science Foundation of China (No. 11471241).The author's work is supported by Ministry of Science and Technology, Taiwan (Grant No. MOST 108-2115-M-003-009-MY2).
Publisher Copyright:
© 2020 Elsevier Inc.

PY - 2021/3/15

Y1 - 2021/3/15

N2 - The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix characterizations for checking the P-property, which is a new approach different from those in the literature. This is a do-able manipulation, which helps verifications of the P-property and globally uniquely solvable (GUS) property in second-order cone linear complementarity problems. Moreover, using an equivalence relation to the second-order cone linear complementarity problem, we study some sufficient and necessary conditions for the unique solution of the absolute value equations associated with second-order cone (SOCAVE).

AB - The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix characterizations for checking the P-property, which is a new approach different from those in the literature. This is a do-able manipulation, which helps verifications of the P-property and globally uniquely solvable (GUS) property in second-order cone linear complementarity problems. Moreover, using an equivalence relation to the second-order cone linear complementarity problem, we study some sufficient and necessary conditions for the unique solution of the absolute value equations associated with second-order cone (SOCAVE).

KW - Absolute value equations

KW - Globally uniquely solvable property

KW - P-property

KW - Second-order cone linear complementarity problem

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U2 - 10.1016/j.laa.2020.11.010

DO - 10.1016/j.laa.2020.11.010

M3 - Article

AN - SCOPUS:85096574737

VL - 613

SP - 271

EP - 294

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -